Week 1: Summary of the key concepts and theories needed to
understand the exercises & Answers to exercises 1.1&1.2
1. The Production of Health
Health is not fixed; it is "produced" using inputs like medical care m, lifestyle
choices l, and time.
• Diminishing Marginal Returns:
o Concept: The first units of an input (like medical care) produce a
large improvement in health. As you add more units, the health
improvement (h) becomes smaller and smaller. This creates a
curved (concave) shape in graphs.
o Marginal Product (MP): This is the additional health gained from
one extra unit of input (e.g., Delta h/ Delta m). Decisions are made
at the margin: you should compare the marginal benefit of the next
unit, not the average.
o Independent Effects: Inputs can affect health independently. For
example, lifestyle (l) might have a constant marginal effect (linear),
while medical care (m) has a diminishing effect.
Mapping:
• Exercise 1.1, Q1a: Calculating marginal effects to see which input is more
productive.
• Exercise 1.1, Q2: Understanding why health production functions differ
between groups (slope vs. intercept) due to supply-side (e.g., doctor skill) or
demand-side (e.g., education) factors.
2. Economic Constraints and Optimization
To maximize health or utility, individuals must navigate limits on their resources.
• Budget Constraint: You cannot spend more than your income (y). If the
price of inputs is 1, the constraint is m + l = y.
• Opportunity Cost: Because resources are scarce, spending money or
time on one thing means giving up something else. The opportunity cost
of medical care is the health or consumption you could have had if you
spent that money on lifestyle or other goods.
• Optimization Rule: To maximize health, you should allocate resources
such that the marginal product per dollar is equal across all inputs. If
MPl > MPm, you should spend more on l.
Mapping:
• Exercise 1.1, Q1b-g: Explaining opportunity cost and using marginal curves to
find the optimal investment.
3. The Grossman Model
This model explains the Demand for Health. People demand health for two
reasons: as a consumption good (to feel good) and as an investment good (to
be healthy enough to work and earn wages).
• Production Possibility Frontier (PPF):
o The PPF shows all feasible combinations of Health (h) and
Consumption (c) an individual can achieve.
1
, o Constraints: The PPF is defined by the Time Constraint (Time is
divided into sick, work, health production, and consumption time)
and the Budget Constraint (Money earned from work pays for
goods).
o Shape: It is a semi-circle (not a straight line) because of
diminishing marginal returns in the production of both health and
consumption.
• Preferences (Indifference Curves):
o Individuals have preferences for both health and consumption,
represented by indifference curves (U). They want to be on the
highest possible curve.
o Optimization: A rational person locates where the PPF touches
the highest indifference curve. They will not choose a point where
both health and consumption can be increased (the rising part of
the PPF) unless they do not value one of them.
2
, • Medical Innovation:
o New technology makes health production more efficient. This
expands the PPF outward (you can get more health for the same
time/money). This leads to both a substitution effect (health is
cheaper, so demand increases) and an income effect (you are
"richer" in resources, so you consume more of both).
Mapping:
• Exercise 1.2, Q1a-d: Identifying constraints and the shape of the PPF.
• Exercise 1.2, Q1e-f: Drawing indifference curves for different preferences.
• Exercise 1.2, Q1g: Analyzing the impact of medical innovation.
4. The Relationship Between Income and Health
There is a strong positive correlation between income and health (The Preston
Curve).
• Diminishing Returns to Income:
o The relationship is non-linear (concave). An increase in income
improves health significantly for the poor, but has a smaller effect
on the rich.
• Income Inequality:
o Because of the diminishing returns, a country with equal income
distribution will have better average health (lower mortality) than a
country with high inequality, even if both have the same average
income. Transferring money from rich to poor gains more health
for the poor than the rich lose.
• Causality:
o Correlation does not prove causation. The relationship could be:
1. Income causes Health.
2. Health causes Income (Reverse causality).
3. Third Factors: Omitted variables like education,
technology, or environment cause both.
Mapping:
• Exercise 1.1, Q3: Explaining diminishing returns and the argument for income
redistribution.
• Exercise 1.1, Q4: How policies (like pollution subsidies) shift the curve versus
moving along it.
• Exercise 1.2, Q2.2-2.3: Analyzing the Preston curve and its shifts over time.
5. Empirical Analysis (Exercises 1.2)
How to quantify these relationships using data.
• Elasticity:
o Measures responsiveness. It is the percentage change in Health
resulting from a 1% change in Income.
o It is estimated using a Double-Log Regression ln(y) vs ln(x). The
coefficient in this regression is the elasticity.
• Fixed Effects:
o A statistical method used with panel data (data over time) to
remove Omitted Variable Bias.
3
, o It controls for time-invariant factors (things that don't change over
time, like a country's geography or culture).
o It cannot control for factors that change over time.
o Mapping:
§ Exercise 1.2, Q2.4: Interpreting regression coefficients as
elasticities and explaining fixed effects.
Exercise 1.1
Question 1
Suppose an individual’s health, h, is produced by medical care, m, and a lifestyle intervention, l.
The health effects of l and m are independent from each other. For each additional unit of l, h
increases by 0.5. The left graph shows this linear relationship between h and l. The right graph
shows the relationship between h and m and is a slightly adapted version of the one used in the
video on the determinants of health. Assume that the money cost of each unit of both l and m
is 1. Income is y, and so the budget constraint is m + l = y.
The health effect of 4 units of m is equal to the effect of 4 units of l. In each case, h increases by
2 units, meaning the average effect of both m and l is 0.5 (Δh/Δm = Δh/Δl = 2/4 = 0.5).
a. From examination of the graphs, at m = l = 4, which of m and l has the largest marginal effect
on health? -- first derivative
The marginal product of l is constant at 0.5. The marginal product of m is 1/2√𝑚. At m=4,
the marginal product of medical care is 1/4 = 0.25, which is smaller than 0.5.
4
understand the exercises & Answers to exercises 1.1&1.2
1. The Production of Health
Health is not fixed; it is "produced" using inputs like medical care m, lifestyle
choices l, and time.
• Diminishing Marginal Returns:
o Concept: The first units of an input (like medical care) produce a
large improvement in health. As you add more units, the health
improvement (h) becomes smaller and smaller. This creates a
curved (concave) shape in graphs.
o Marginal Product (MP): This is the additional health gained from
one extra unit of input (e.g., Delta h/ Delta m). Decisions are made
at the margin: you should compare the marginal benefit of the next
unit, not the average.
o Independent Effects: Inputs can affect health independently. For
example, lifestyle (l) might have a constant marginal effect (linear),
while medical care (m) has a diminishing effect.
Mapping:
• Exercise 1.1, Q1a: Calculating marginal effects to see which input is more
productive.
• Exercise 1.1, Q2: Understanding why health production functions differ
between groups (slope vs. intercept) due to supply-side (e.g., doctor skill) or
demand-side (e.g., education) factors.
2. Economic Constraints and Optimization
To maximize health or utility, individuals must navigate limits on their resources.
• Budget Constraint: You cannot spend more than your income (y). If the
price of inputs is 1, the constraint is m + l = y.
• Opportunity Cost: Because resources are scarce, spending money or
time on one thing means giving up something else. The opportunity cost
of medical care is the health or consumption you could have had if you
spent that money on lifestyle or other goods.
• Optimization Rule: To maximize health, you should allocate resources
such that the marginal product per dollar is equal across all inputs. If
MPl > MPm, you should spend more on l.
Mapping:
• Exercise 1.1, Q1b-g: Explaining opportunity cost and using marginal curves to
find the optimal investment.
3. The Grossman Model
This model explains the Demand for Health. People demand health for two
reasons: as a consumption good (to feel good) and as an investment good (to
be healthy enough to work and earn wages).
• Production Possibility Frontier (PPF):
o The PPF shows all feasible combinations of Health (h) and
Consumption (c) an individual can achieve.
1
, o Constraints: The PPF is defined by the Time Constraint (Time is
divided into sick, work, health production, and consumption time)
and the Budget Constraint (Money earned from work pays for
goods).
o Shape: It is a semi-circle (not a straight line) because of
diminishing marginal returns in the production of both health and
consumption.
• Preferences (Indifference Curves):
o Individuals have preferences for both health and consumption,
represented by indifference curves (U). They want to be on the
highest possible curve.
o Optimization: A rational person locates where the PPF touches
the highest indifference curve. They will not choose a point where
both health and consumption can be increased (the rising part of
the PPF) unless they do not value one of them.
2
, • Medical Innovation:
o New technology makes health production more efficient. This
expands the PPF outward (you can get more health for the same
time/money). This leads to both a substitution effect (health is
cheaper, so demand increases) and an income effect (you are
"richer" in resources, so you consume more of both).
Mapping:
• Exercise 1.2, Q1a-d: Identifying constraints and the shape of the PPF.
• Exercise 1.2, Q1e-f: Drawing indifference curves for different preferences.
• Exercise 1.2, Q1g: Analyzing the impact of medical innovation.
4. The Relationship Between Income and Health
There is a strong positive correlation between income and health (The Preston
Curve).
• Diminishing Returns to Income:
o The relationship is non-linear (concave). An increase in income
improves health significantly for the poor, but has a smaller effect
on the rich.
• Income Inequality:
o Because of the diminishing returns, a country with equal income
distribution will have better average health (lower mortality) than a
country with high inequality, even if both have the same average
income. Transferring money from rich to poor gains more health
for the poor than the rich lose.
• Causality:
o Correlation does not prove causation. The relationship could be:
1. Income causes Health.
2. Health causes Income (Reverse causality).
3. Third Factors: Omitted variables like education,
technology, or environment cause both.
Mapping:
• Exercise 1.1, Q3: Explaining diminishing returns and the argument for income
redistribution.
• Exercise 1.1, Q4: How policies (like pollution subsidies) shift the curve versus
moving along it.
• Exercise 1.2, Q2.2-2.3: Analyzing the Preston curve and its shifts over time.
5. Empirical Analysis (Exercises 1.2)
How to quantify these relationships using data.
• Elasticity:
o Measures responsiveness. It is the percentage change in Health
resulting from a 1% change in Income.
o It is estimated using a Double-Log Regression ln(y) vs ln(x). The
coefficient in this regression is the elasticity.
• Fixed Effects:
o A statistical method used with panel data (data over time) to
remove Omitted Variable Bias.
3
, o It controls for time-invariant factors (things that don't change over
time, like a country's geography or culture).
o It cannot control for factors that change over time.
o Mapping:
§ Exercise 1.2, Q2.4: Interpreting regression coefficients as
elasticities and explaining fixed effects.
Exercise 1.1
Question 1
Suppose an individual’s health, h, is produced by medical care, m, and a lifestyle intervention, l.
The health effects of l and m are independent from each other. For each additional unit of l, h
increases by 0.5. The left graph shows this linear relationship between h and l. The right graph
shows the relationship between h and m and is a slightly adapted version of the one used in the
video on the determinants of health. Assume that the money cost of each unit of both l and m
is 1. Income is y, and so the budget constraint is m + l = y.
The health effect of 4 units of m is equal to the effect of 4 units of l. In each case, h increases by
2 units, meaning the average effect of both m and l is 0.5 (Δh/Δm = Δh/Δl = 2/4 = 0.5).
a. From examination of the graphs, at m = l = 4, which of m and l has the largest marginal effect
on health? -- first derivative
The marginal product of l is constant at 0.5. The marginal product of m is 1/2√𝑚. At m=4,
the marginal product of medical care is 1/4 = 0.25, which is smaller than 0.5.
4
